Jost, Jürgen and Wang, Ying (2014) Optimization and phenotype allocation. Bulletin of Mathematical Biology, Volume 76 (Number 1). pp. 184-200. doi:10.1007/s11538-013-9915-5

Research output not available from this repository, contact author.

Request Changes to record.

Abstract

We study the phenotype allocation problem for the stochastic evolution of a multitype population in a random environment. Our underlying model is a multitype Galton–Watson branching process in a random environment. In the multitype branching model, different types denote different phenotypes of offspring, and offspring distributions denote the allocation strategies. Two possible optimization targets are considered: the long-term growth rate of the population conditioned on nonextinction, and the extinction probability of the lineage. In a simple and biologically motivated case, we derive an explicit formula for the long-term growth rate using the random Perron–Frobenius theorem, and we give an approximation to the extinction probability by a method similar to that developed by Wilkinson. Then we obtain the optimal strategies that maximize the long-term growth rate or minimize the approximate extinction probability, respectively, in a numerical example. It turns out that different optimality criteria can lead to different strategies.

Item Type:	Journal Article
Divisions:	Faculty of Science > Centre for Systems Biology
Journal or Publication Title:	Bulletin of Mathematical Biology
Publisher:	Springer New York LLC
ISSN:	0092-8240
Official Date:	1 January 2014
Dates:	Date Event 1 January 2014 Published
Volume:	Volume 76
Number:	Number 1
Page Range:	pp. 184-200
DOI:	10.1007/s11538-013-9915-5
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

Request changes or add full text files to a record

Repository staff actions (login required)

View Item